For which of the following curves, the line \[x + \sqrt 3 y = 2\sqrt 3 \] is the tangent at the point \[\left( {{{3\sqrt 3 } \over 2},{1 \over 2}} \right)\]?
Solutions · 1
Official solution
Tangent to x2+9y2=9 at
point \[\left( {{{3\sqrt 3 } \over 2},{1 \over 2}} \right)\] is \[x\left( {{{3\sqrt 3 } \over 2}} \right) + 9y\left( {{1 \over 2}} \right) = 9\]
\[3\sqrt 3 x + 9y = 18 \Rightarrow x + \sqrt 3 y = 2\sqrt 3 \]
\[ \Rightarrow \] option (1) is true.